2021/06/01 by Alberto Del Pia, Del Pia, Alberto, Jeff Linderoth +3
Engineering · Mathematics · #FOS: Mathematics #Industrial Vision Systems and Defect Detection #Manufacturing Process and Optimization #Optimization and Control (math.OC) #Optimization and Packing Problems #math.OC
paper · pdf · doi:10.48550/arxiv.2106.00301
openalex publication_date 2021/06/01 · arxiv created 2021/11/22 · arxiv updated 2021/11/23 · openalex created_date 2022/11/01 · openalex updated_date 2026/07/28
We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and study the structure of a totally-ordered multiple knapsack set. The valid multi-cover inequalities we derive for its convex hull have a number of interesting properties. First, they generalize the well-known (1, k)-configuration inequalities. Second, they are not aggregation cuts. Third, they cannot be generated as a rank-1 Chvatal-Gomory cut from the inequality system consisting of the knapsack constraints and all their minimal cover inequalities. We also provide conditions under which the inequalities are facets for the convex hull of the totally-ordered knapsack set, as well as conditions for those inequalities to fully characterize its convex hull. We give an integer program to solve the separation and provide numerical experiments that showcase the strength of these new inequalities.